Lesson Title: Wavelength, Frequency, Speed of Sound in And Speed of Sound in Air, Water and Solids
State Standards: GLEs/GSEs
See Unit
National Standards:
See Unit
Context of Lesson:
We have learned that sound waves can travel through a gas, a liquid, or a solid, and have several modes of travel, not all available in all materials. This lesson looks at what determines the speed of wave travel.
Opportunities to Learn:
Depth of Knowledge
DoK1 Units of measurement and definitions.
Prerequisite Knowledge
Introduction to wave motion
Plans for Differentiating Instruction
Explanations are all conceptual, with mathematic version as advanced option.
Accommodations and modifications
Dynamic real time graph representation of actual physical system.
Variety of musical instruments for hands on experimentation.
Lab teams can pair special need student with another student helper.
Environmental factors
none
Materials
Speaker, sound generator, microphones, computer and (free) software
Assorted musical instruments (slide whistles, pan pipes, guitars or ukeleles)
Digital Tuner (frequency meter)
If possible, one setup for each lab should be instrumented with e.g. Vernier Labview or Pasco Probeware so nthat students can see the graphs develop as the experimental system operates.
This could best be used as part of the lecture.
It would also be good as the attention getter for the opening remarks.
It is not needed for every student station, but could be useful for additional support to some students, as needed.
Objectives:
Students will be able to
explain how sound speed may be measured
explain creation of standing waves
explain resonance
offer examples of resonance in various musical instruments
Instruction:
Opening:
The first demo setup is a sound source, a small speaker, and two microphones, one near it and one further away.
A computer shows two pulses when the speaker makes a click, one from each.
This can run steadily, making a click every few seconds, and showing a new trace.
If possible, put it up on a projection screen or smart board.
(I don't know how yet, but sure this is practical.)
This can run while attendance and other business is taken care of.
Engagement:
We have learned about different modes of wave travel.
Today we would like to learn how fast sound waves travel, and what might influence that speed.
We can measure sound speed by sending a sound over some known distance, and measuring how long it takes to get there.
We would like the distance to be long enough that we can measure the time accurately.
Say we can measure one second accurately. In one second a sound travels about a thousand feet or three hundred meters.
So we would have to go outside to find a large enough space, Measuring one second would still be subject to error due to our reaction time, so we would prefer a longer path, but that would also require a louder noise. So a simple measurement becomes a big project
This was done hundreds of years ago. Galileo described the method, which was already well understood.
"When we see a piece of artillery fired at great distance, the flash reaches our eyes without delay; but the sound reaches the ear only after a noticeable interval."
Until recently, this was the only way to do it. We are now able to easily measure travel time more accurately, as this shows.
So, let's determine the speed of sound.
What is the distance to the remote microphone? Meter stick.
What is the delay time at the second microphone? Time scale on display.
Distance over time is what number and what units?
Remark, we could do this in water too, but it would be more trouble. We would need
a long water tank
water proof sound source and microphones
accuarte timing for the higher speed and shorter travel time
(( Might work to use a hose filled with water. It could be looped instead of straight, which might cause some error. Need to protect the speaker and microphones. I have not tried this, but want to. It would be nice ... ))
Remark, just by similarity to Simple Harmonic Motion, we might expect a stronger restoring force to give faster wave speed, and a heavier mass density to give a slower speed. That turns out to be true.
And we might expect yhe Amplitude to have no effect on speed. That turns out to be true as well.
We know that every system of SHM has a natural frequency, but can be forced to move at any other frequency.
So we might ask, again, just by similarity to Simple Harmonic Motion, if a fluid has a "best" frequency, at which the speed is higher? But that turns out to be false.
Now, by moving the "distant" microphone to be next to the sound source, and pointing both at the wall, we can see an echo.
As we move further from the wall, the time increases.
We have used distance probes in some of our experiments. This is how they work.
Show one and move something toward and away from it.
The next setup is an open tube standing in a tall graduate cylinder filled with water.
By raising the tube we leave an air space above the water surface,
If you hold a tuning fork over this open tube, so that sound can enter, there will be an echo from the water surface.
Try this with different lengths and see what you notice.
When the echo comes back to the source at just the right time, the two sounds add together, and result in a louder sound.
Finally, it is your turn.
We have some simple musical instruments. This part is a Lab, so fill out a report as always, for each setup.
That means a clearly labeled diagram, a data table, and conclusions.
Slide whistle. How does the sound relate to the position of the slide?
Pan pipes. How does each pipe sound?
Drum. What happens if you tighten the drum head? Hit it in different places?
Guitar, or Ukelele, or Dulcimer. Here there are several thngs to try.
How does each string look, and how does it sound?
How does the sound change if you shorten the string by holding it down?
How does a string sound if change the tension?
What have you observed?
Similarities in Most or All?
Differences?
Surprises?
Some instruments have a fixed note for each part and a choice of parts.
Some instruments have quickly adjustable note from the same part.
As always, save your lab report as a study guide.
We'll grade them at the end of the unit.
Differentiated Instruction
(This is not done, still needs a graphic, but a place holder for the optional advanced part, to come.) The derivations are taken fom Sears and Zemansky, University Physics, Addison - Wesley, 1964. In a fluid, which could be either air or a liquid, waves travel as compression and relaxation regions traveling along the path.
Looking at a compression, it is a region of air where the normally random molecular vibration has an excess of momentum in one direction, the direction of travel. As collisions transfer this momentum, which can also be thought of as a force, the compression region travels. Since the transfer of momentum is also a transfer of energy, thie energy travels too. The speed is found to be determined by two factors, the compressibility and the density of the air.
Consider a tube with cross sectional area A, holding a fluid at pressure P, which has a density rho at the current pressure, and a Bulk Modulus B defined as the ratio of the extra pressure required to compress the fluid, over the fractional compression resulting. That is,
B = dPressure / (dVolume / Volume)
Now consider the extra pressure dP to be applied to the end of the tube, say by a closely fitted piston of area A, which moves into the tube at velocity v.
After a short time t, the piston has moved a distance vt into the tube, and the fluid in a thin region ahead of it, which we can think of as the wave front, also has been given the velocity v.
Fluid further away has not yet been influenced and has zero velocity.
We want to find the speed c at which the wave front advances.
At this time t, the wave front region extends to distance ct from the starting point, but the piston has already moved to vt, so there has been a compression of v/c which is true for length, and also for volume, with constant area A.
The wave front region had an original volume of Act, thus a mass of Act * rho, and still has that mass, now compressed.
Using the relation that Impulse (force * time) equals change in momentum (m * v) we can write
A * B * (v/c) * t = rho * A * t * c * v
which simplifies to
c = sqrt (B / rho)
that is,
c = sqrt ( Bulk Modulus / Density)
A large value for Bulk Modulus means a "stiffer" fluid, which we would expect to transfer a wave more quickly,
while a large rho means a "heavier" fluid, which we expect to respond more slowly. ( really need to learn type setting equations. Must be a way. Yes there is.)
We can use a similar method for a transverse wave on a string.
Here the wave is a small part of the string that is stretched away from the normal straight line.
As this displacement moves along the string, each part must be accelerated away from rest, then restored by the tension in the string.
Consider the string to have a linear density mu of mass / length, and be under a stretching force of S.
A transverse force F has been applied and a short interval t has gone by, during this time the disturbance has advanced a distance ct, where c is the wave propagation speed we want to determine.
Within the section of string that has been influenced, the transverse speed is v .
Comparing the forces F and S, we have (v / c) = (F / S) or v = c * (F/S)
Since impulse applied to this string section equals it's change in momentum
S * (v/c) * t = v * c * t * mu
which simplifies to
c = sqrt (S/mu)
Thus, wave speed depends on two factors, the tension applied to the string and the mass per unit length, or linear density.
As we expect, more tension causes a faster advance, higher density a slower advance.
Closure:
We have measured sound speed in air, and at least talked about how we could measure sound speed in water.
We have seen how an echo in a space of the right length can produce a standing wave, and a condition called resonance.
We have seen examples of resonance in some musical instruments.
Don't Forget to bring an Instrument Next Time (If You Want To)
Do you play an instrument? Would you be willing to bring it, show it and explain it, and of course, play it for us?
Real instruments have a more interesting sound than a single frequency tone.
We will be looking at wave forms to see why.
Lesson Plan
Lesson Title: Wavelength, Frequency, Speed of Sound in And Speed of Sound in Air, Water and Solids
State Standards: GLEs/GSEs
See Unit
National Standards:
See Unit
Context of Lesson:
We have learned that sound waves can travel through a gas, a liquid, or a solid, and have several modes of travel, not all available in all materials.This lesson looks at what determines the speed of wave travel.
Opportunities to Learn:
Depth of Knowledge
DoK1 Units of measurement and definitions.
Prerequisite Knowledge
Introduction to wave motion
Plans for Differentiating Instruction
Explanations are all conceptual, with mathematic version as advanced option.
Accommodations and modifications
Dynamic real time graph representation of actual physical system.
Variety of musical instruments for hands on experimentation.
Lab teams can pair special need student with another student helper.
Environmental factors
none
Materials
Speaker, sound generator, microphones, computer and (free) software
Assorted musical instruments (slide whistles, pan pipes, guitars or ukeleles)
Digital Tuner (frequency meter)
If possible, one setup for each lab should be instrumented with e.g. Vernier Labview or Pasco Probeware so nthat students can see the graphs develop as the experimental system operates.
Objectives:
Students will be able to
Instruction:
Opening:
The first demo setup is a sound source, a small speaker, and two microphones, one near it and one further away.
A computer shows two pulses when the speaker makes a click, one from each.
This can run steadily, making a click every few seconds, and showing a new trace.
If possible, put it up on a projection screen or smart board.
(I don't know how yet, but sure this is practical.)
This can run while attendance and other business is taken care of.
Engagement:
We have learned about different modes of wave travel.
Today we would like to learn how fast sound waves travel, and what might influence that speed.
We can measure sound speed by sending a sound over some known distance, and measuring how long it takes to get there.
We would like the distance to be long enough that we can measure the time accurately.
Say we can measure one second accurately. In one second a sound travels about a thousand feet or three hundred meters.
So we would have to go outside to find a large enough space, Measuring one second would still be subject to error due to our reaction time, so we would prefer a longer path, but that would also require a louder noise. So a simple measurement becomes a big project
This was done hundreds of years ago. Galileo described the method, which was already well understood.
"When we see a piece of artillery fired at great distance, the flash reaches our eyes without delay; but the sound reaches the ear only after a noticeable interval."
Until recently, this was the only way to do it. We are now able to easily measure travel time more accurately, as this shows.
So, let's determine the speed of sound.
Remark, we could do this in water too, but it would be more trouble. We would need
(( Might work to use a hose filled with water. It could be looped instead of straight, which might cause some error. Need to protect the speaker and microphones. I have not tried this, but want to. It would be nice ... ))
Remark, just by similarity to Simple Harmonic Motion, we might expect a stronger restoring force to give faster wave speed, and a heavier mass density to give a slower speed. That turns out to be true.
And we might expect yhe Amplitude to have no effect on speed. That turns out to be true as well.
We know that every system of SHM has a natural frequency, but can be forced to move at any other frequency.
So we might ask, again, just by similarity to Simple Harmonic Motion, if a fluid has a "best" frequency, at which the speed is higher? But that turns out to be false.
Now, by moving the "distant" microphone to be next to the sound source, and pointing both at the wall, we can see an echo.
As we move further from the wall, the time increases.
We have used distance probes in some of our experiments. This is how they work.
Show one and move something toward and away from it.
The next setup is an open tube standing in a tall graduate cylinder filled with water.
By raising the tube we leave an air space above the water surface,
If you hold a tuning fork over this open tube, so that sound can enter, there will be an echo from the water surface.
Try this with different lengths and see what you notice.
When the echo comes back to the source at just the right time, the two sounds add together, and result in a louder sound.
Finally, it is your turn.
We have some simple musical instruments. This part is a Lab, so fill out a report as always, for each setup.
That means a clearly labeled diagram, a data table, and conclusions.
What have you observed?
Some instruments have a fixed note for each part and a choice of parts.
Some instruments have quickly adjustable note from the same part.
As always, save your lab report as a study guide.
We'll grade them at the end of the unit.
Differentiated Instruction
(This is not done, still needs a graphic, but a place holder for the optional advanced part, to come.)
The derivations are taken fom Sears and Zemansky, University Physics, Addison - Wesley, 1964.
In a fluid, which could be either air or a liquid, waves travel as compression and relaxation regions traveling along the path.
Looking at a compression, it is a region of air where the normally random molecular vibration has an excess of momentum in one direction, the direction of travel. As collisions transfer this momentum, which can also be thought of as a force, the compression region travels. Since the transfer of momentum is also a transfer of energy, thie energy travels too. The speed is found to be determined by two factors, the compressibility and the density of the air.
Consider a tube with cross sectional area A, holding a fluid at pressure P, which has a density rho at the current pressure, and a Bulk Modulus B defined as the ratio of the extra pressure required to compress the fluid, over the fractional compression resulting. That is,
B = dPressure / (dVolume / Volume)
Now consider the extra pressure dP to be applied to the end of the tube, say by a closely fitted piston of area A, which moves into the tube at velocity v.
After a short time t, the piston has moved a distance vt into the tube, and the fluid in a thin region ahead of it, which we can think of as the wave front, also has been given the velocity v.
Fluid further away has not yet been influenced and has zero velocity.
We want to find the speed c at which the wave front advances.
At this time t, the wave front region extends to distance ct from the starting point, but the piston has already moved to vt, so there has been a compression of v/c which is true for length, and also for volume, with constant area A.
The wave front region had an original volume of Act, thus a mass of Act * rho, and still has that mass, now compressed.
Using the relation that Impulse (force * time) equals change in momentum (m * v) we can write
A * B * (v/c) * t = rho * A * t * c * v
which simplifies to
c = sqrt (B / rho)
that is,
c = sqrt ( Bulk Modulus / Density)
A large value for Bulk Modulus means a "stiffer" fluid, which we would expect to transfer a wave more quickly,
while a large rho means a "heavier" fluid, which we expect to respond more slowly.
( really need to learn type setting equations. Must be a way. Yes there is.)
We can use a similar method for a transverse wave on a string.
Here the wave is a small part of the string that is stretched away from the normal straight line.
As this displacement moves along the string, each part must be accelerated away from rest, then restored by the tension in the string.
Consider the string to have a linear density mu of mass / length, and be under a stretching force of S.
A transverse force F has been applied and a short interval t has gone by, during this time the disturbance has advanced a distance ct, where c is the wave propagation speed we want to determine.
Within the section of string that has been influenced, the transverse speed is v .
Comparing the forces F and S, we have (v / c) = (F / S) or v = c * (F/S)
Since impulse applied to this string section equals it's change in momentum
S * (v/c) * t = v * c * t * mu
which simplifies to
c = sqrt (S/mu)
Thus, wave speed depends on two factors, the tension applied to the string and the mass per unit length, or linear density.
As we expect, more tension causes a faster advance, higher density a slower advance.
Closure:
We have measured sound speed in air, and at least talked about how we could measure sound speed in water.
We have seen how an echo in a space of the right length can produce a standing wave, and a condition called resonance.
We have seen examples of resonance in some musical instruments.
Don't Forget to bring an Instrument Next Time (If You Want To)
Do you play an instrument? Would you be willing to bring it, show it and explain it, and of course, play it for us?
Real instruments have a more interesting sound than a single frequency tone.
We will be looking at wave forms to see why.
Assessment:
Participation.
Lab reports are graded at end of unit.
Reflections
(only done after lesson is enacted)Student Work Sample 1 – Approaching Proficiency:
Student Work Sample 2 – Proficient:
Student Work Sample 3 – Exceeds Proficiency: